A combined boundary integral and Lambert's Law method for modelling multibeam backscatter data from the seafloor

•Wave equation solution of seafloor backscatter uses boundary integral and Lambert's Law.•Solution is compared to finite-difference calculations over a range of seafloor roughness.•Forwarded model calculations use roughness length scales, amplitude, and hardness.•Our solution can be used to invert angular backscatter response to classify seafloor types.

A theory has been developed to model multibeam acoustic swath backscatter angular response for a two-dimensional seafloor using a combination of a boundary integral and a Lambert's Law approximation. In this theoretical approach the seafloor topography is assumed to affect scattering at two different scales: a random distribution of surface roughness (mm to cm) over small spatial distances causes scattering, while the undulating seafloor morphology at larger distances (up to 10 s of m) affects the angles of incidence of the acoustic energy with the seabed. The latter distance scales are comparable to the resolution of bathymetry acquired by commercial multibeam sonars in shelf seas, so this variation can be directly measured, leaving the small-roughness scale, not practically measureable, to be modelled by random variation. The method applies to a two-dimensional seafloor model where the bathymetry is invariant in a direction perpendicular to the multibeam swath but its physical properties (acoustic impedance, roughness amplitude and correlation length) can vary laterally across-track. We demonstrate the boundary integral technique for a range of seafloors with differing roughness. We validate our results using a time-domain finite-difference solution to the acoustic wave equation, the composite roughness model of seafloor backscattering, and comparison of observed multibeam data across contrasting fine-grained sand to course shell hash seafloor transition in Galway Bay, Ireland.